Toward a mathematical theory of behavioral-social dynamics for pedestrian crowds

Bellomo, Nicola; Gibelli, Livio

doi:10.1142/s0218202515400138

Cited by 110 publications

(80 citation statements)

References 30 publications

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“…Hence, one also has to look for a multiscale validity of the entropy function by looking at it as a tool that can contribute to the qualitative analysis of mathematical problems [53]. Segregation phenomena in swarms and crowds means subdivision into different groups sharing a certain behavior (e.g., multilane fingering in crowd dynamics as studied in [11]). It can be a local phenomenon, and hence it might require the definition of a local Entropy function.…”

Section: Research Perspectivesmentioning

confidence: 99%

“…The interested reader is referred to the book [3] for theoretical aspects and for the rationale to develop specific applications which have been produced to model, for instance, the dynamics of collective learning [4], the immune competition [5], vehicular traffic [6][7][8], the dynamics of crowds [9][10][11], and the collective motion of swarms [12].…”

Section: Introductionmentioning

confidence: 99%

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On Entropy Dynamics for Active “Living” Particles

Ełaiw

Alghamdi

Bellomo

2017

Entropy

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This paper presents a modeling approach, followed by entropy calculations of the dynamics of large systems of interacting active particles viewed as living-hence, complex-systems. Active particles are partitioned into functional subsystems, while their state is modeled by a discrete scalar variable, while the state of the overall system is defined by a probability distribution function over the state of the particles. The aim of this paper consists of contributing to a further development of the mathematical kinetic theory of active particles.

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Section: Research Perspectivesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Entropy Dynamics for Active “Living” Particles

Ełaiw

Alghamdi

Bellomo

2017

Entropy

Self Cite

View full text Add to dashboard Cite

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“…Based on knowledge of various indoor spaces, the majority of models can be divided into macroscopic [3,4] and microscopic models [5][6][7][8][9][10][11][12]. Additionally, based on kinetic theory, some scholars have proposed mesoscopic models [13,14], which consider how heterogeneous individual behaviors can modify collective dynamics. Most macroscopic models use network simulations [15][16][17][18][19], while the other models use grid simulations [20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Modeling of Macroscopic Building Evacuation Using IFC Data

Zhu

Zhou

Zhang

et al. 2018

IJGI

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Abstract:Presently, most models of crowd evacuations within a building are created manually. This is inefficient. To address this issue, this paper focuses on the differences and relationship between industry foundation classes (IFC) and the macroscopic network model for evacuation (MNME), and studies the mapping and construction methods used to convert entity objects into nodes and arcs in the MNME. Furthermore, corresponding attribute information in the MNME are established from IFC. Based on this process, the MNME is created and used as an input to EVACNET4 to obtain simulation results. Finally, the results, together with a 3D building model, are expressed in a unified environment. Our study results show that a network as well as the relevant attributes can be automatically generated from IFC, and can be adapted to different working conditions. The method proposed in this paper can automatically map the semantic information model to the MNME and the simulation result as well as the building model can be integrated in a Geographic Information System (GIS) environment.

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“…These artifacts can be reduced by incorporating extra rules and/or elaborate calibrations, at the price of an increased computational cost.The scale of observation for the third approach is between the previous two. Introduced in [5] and further developed in [1, 6,7,9,10,11,12], this approach derives a Boltzmann-type evolution equation for the statistical distribution function of the position and velocity of the pedestrians, in a framework close to that of the kinetic theory of gases. See also [13] for a literature review on this approach.…”

mentioning

confidence: 99%

“…See also [13] for a literature review on this approach. The model proposed in [5, 6,12] is valid in unbounded domains and with a homogeneous distribution of walking ability for the pedestrians, while the extension to bounded domains is presented in [1] and further explored in [9,10,11]. In [9], more general features of behavioral-social dynamics are taken into account.…”

mentioning

confidence: 99%

A kinetic theory approach to model pedestrian dynamics in bounded domains with obstacles

Kim¹,

Quaini²

2019

Kinetic &Amp; Related Models

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We consider a kinetic theory approach to model the evacuation of a crowd from bounded domains. The interactions of a person with other pedestrians and the environment, which includes walls, exits, and obstacles, are modeled by using tools of game theory and are transferred to the crowd dynamics. The model allows to weight between two competing behaviors: the search for less congested areas and the tendency to follow the stream unconsciously in a panic situation. For the numerical approximation of the solution to our model, we apply an operator splitting scheme which breaks the problem into two pure advection problems and a problem involving the interactions. We compare our numerical results against the data reported in a recent empirical study on evacuation from a room with two exits. For medium and medium-to-large groups of people we achieve good agreement between the computed average people density and flow rate and the respective measured quantities. Through a series of numerical tests we also show that our approach is capable of handling evacuation from a room with one or more exits with variable size, with and without obstacles, and can reproduce lane formation in bidirectional flow in a corridor. arXiv:1901.07620v3 [math.NA] 14 Jun 2019 density and linear momentum, which are regarded as macroscopic observables of pedestrian flow. See, e.g., [28,37]. Such an approach is suitable for high density, large-scale systems, which are not the focus of our work.A second approach looks at the problem at the microscopic level. Microscopic models can be further divided into models which are grid-based or grid-free. Cellular Automata [14,15,16,21,31] models belong to the first category. They describe pedestrian flow in space-time by assigning discrete states to a grid of space-cells. These cells can be occupied by a pedestrian or be empty. Thus, the movement of pedestrians in space is done by passing them from cell to cell (discrete space) in discrete time. Grid-free methods can be based on second order models (forces-based), first order models (vision-based or speed-based) or zeroth order models (rule-based or decision-based). Forcebased models use Newtonian mechanics to interpret pedestrian movement as the physical interaction between the people and the environment, i.e. the action of other people and the environment on a given pedestrian is modeled with forces. These models are one of the most popular modeling paradigms of continuous models because they describe the movement of pedestrians qualitatively well. See, e.g., [18,24,26,27,32,33,39,43] and references therein. Collective phenomena, like unidirectional or bidirectional flow in a corridor, lane formation, oscillations at bottlenecks, the faster-is-slower effect, and emergency evacuation from buildings, are well reproduced. Agentbased models allow for flexibility, extensibility, and capability to realize heterogeneity in crowd dynamics. For examples of vision-based, speed-based, rule-based, and decision-based models we refer to [2,3, 4,17,19,20] and references t...

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Toward a mathematical theory of behavioral-social dynamics for pedestrian crowds

Cited by 110 publications

References 30 publications

On Entropy Dynamics for Active “Living” Particles

On Entropy Dynamics for Active “Living” Particles

Modeling of Macroscopic Building Evacuation Using IFC Data

A kinetic theory approach to model pedestrian dynamics in bounded domains with obstacles

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